Order-restricted Bayesian Inference with Applications to Human Fertility Studies

• Activity Number: 289
• Type: Invited
• Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): David B. Dunson*+
• Companies: National Institute of Environmental Health Sciences
• Keywords: Bayesian methods ; latent variables ; parameter restrictions ; variable selection priors ; stochastic search ; nonlinear modeling

Abstract

In many biomedical studies, there is interest in the association between an ordered categorical predictor and a discrete outcome, and it is plausible to assume a priori that the mean is nondecreasing across levels of the categorical predictor. Such order restrictions can greatly improve estimation efficiency and power to detect an association. Motivated by fertility applications, this article proposes a general Bayesian approach for inferences on ordered trends in count, binary, and aggregated binary data. A class of latent count models is proposed, which accommodates a broad variety of data structures while facilitating parameter interpretation and computation. Order restrictions are incorporated through a mixture prior which has restricted support and assigns positive probability to the null hypothesis of no association. This prior is conditionally conjugate after data augmentation, resulting in simple and efficient posterior computation. The methods are applied to studies of predictors of the day-specific probabilities of pregnancy in relation to the estimated day of ovulation.